Search

This paper concerns the invasion dynamics of the lattice pioneerclimax competition model with parameter regions in which the system is non-monotone. We estimate the spreading speeds and establish appropriate conditions under which the spreading speeds are linearly selected. Moreover, the existence of travelling waves is determined by constructing suitable upper and lower solutions. It shows that the spreading speed coincides with the minimum wave speed of travelling waves if the diffusion rate of the invasive species is larger or equal to that of the native species. Our results are new to estimate the spreading speed of non-monotone lattice pioneer-climax systems, and the techniques developed in this work can be used to study the invasion dynamics of the pioneer-climax system with interaction delays, which could extend the results in the literature. The analysis replies on the construction of auxiliary systems, upper and lower solutions, and the monotone dynamical system approach. [ABSTRACT FROM AUTHOR]

We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically. [ABSTRACT FROM AUTHOR]

A fifth-order nonlinear wave equation (generalized Korteweg–deVries equation) that arises in the theory of thin liquid films is introduced with the odd viscosity by the long-wave approximation regime. The presence of the odd viscosity is considered to be a non-dissipative factor in the evolution of the film flow. Sinusoidal and travelling waves arise in systems with non dissipation and instability. The introduced wave equation includes quadratic and cubic nonlinearities. The linear instability of sinusoidal waves is analyzed. The stability and bifurcation of travelling waves are discussed. [ABSTRACT FROM AUTHOR]

In this work we study travelling wave solutions to bistable reaction–diffusion equations on bi-infinite k-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction–diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formulas to bound the thin region in parameter space where the propagation direction undergoes a reversal.

The aim of this paper is to study the nonlinear couple Drinfel’d–Sokolov–Wilson (DSW) equation under conformable differential operator (CDO) that plays an important role in describing the shallow water in fluid mechanics, plasma physics, nonlinear optics and Bose–Einstein condensate (soliton formation). The Tanh–Coth and energy balance techniques are implemented in this work to explore some travelling wave solutions. These analytical methods yield various solutions for the considered DSW equation. The solutions obtained from both method are expressed in the form of hyperbolic and trigonometric function. Furthermore, the dynamic behaviour of the obtained solutions are illustrated, via 2D and 3D curves. Additionally, the effect of the conformable differential operator on dynamics of wave solutions is studied via 2D graphs.

We propose an alpha-beta-point non-linear boundary value problem that involves both Caputo derivatives and RL integrals, such that its limiting-case on the parameters alpha and beta product a fourth order problem that arises in bridge design. We begin first by presenting a uniqueness of solution result for the problem. Then, the Ulam-Hyers stability is discussed. An example is then discussed. Also, in a second part, we apply the tanh method for finding travelling waves for a nonlinear problem that involves Khalil derivatives in time and space. Some graphs are plotted for the obtained travelling waves. [ABSTRACT FROM AUTHOR]

A new approach to calculations based on the modal synthesis method is proposed for the evaluation of structural and dry-friction damping effects on self-excited vibrations due to aeroelastic instability in bladed turbine wheels. The method described herein is used to study dry-friction damping of self-excited vibration of an industrial turbine wheel with 66 blades. For evaluating damping effects, the blade couplings are applied to this particular turbine wheel. Therefore, neighbouring blades are interconnected by rigid arms that are fixed on one side to one blade and are in frictional contact on their free side with the other blade. Due to relatively normal motions in contacts, the prescribed contact forces vary over time. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. In this paper, we attempt to model flow-induced instabilities with the Van der Pol model linked to relative motion between neighbouring blades. The proposed modal synthesis method as ROM is a computationally efficient solution allowing substantial parametrization. The effect of the angles of contact surfaces on the wheel dynamics and on the level of the self-excitation suppression will be discussed herein. [ABSTRACT FROM AUTHOR]

The main goal of the presented study is to introduce a model of a pairwise invasion interaction with a nonlinear diffusion and advection. The new equation is based on the further general works introduced by Bramson (1988) to describe the invasive-invaded dynamics. This type of model is made particular with a density dependent diffusion along with an advection term. The new resulting model is then analyzed to explore the regularity, existence and uniqueness of solutions. It is well known that density dependent diffusion operators induce a propagating front with finite speed for compactly supported functions. Based on this, we introduce an analytical approach to determine the evolution of such a propagating front in the invasion dynamics. Afterward, we study the problem with travelling wave profiles and a numerical assessment. As a main finding to remark: When both species propagate with significantly different travelling wave speeds, the interaction becomes unstable, while when the species propagate with similar low speeds, the interaction stabilizes.

A new approach to calculations based on the modal synthesis method is proposed for the evaluation of structural and dry-friction damping effects on self-excited vibrations due to aeroelastic instability in bladed turbine wheels. The method described herein is used to study dry-friction damping of self-excited vibration of an industrial turbine wheel with 66 blades. For evaluating damping effects, the blade couplings are applied to this particular turbine wheel. Therefore, neighbouring blades are interconnected by rigid arms that are fixed on one side to one blade and are in frictional contact on their free side with the other blade. Due to relatively normal motions in contacts, the prescribed contact forces vary over time. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. In this paper, we attempt to model flow-induced instabilities with the Van der Pol model linked to relative motion between neighbouring blades. The proposed modal synthesis method as ROM is a computationally efficient solution allowing substantial parametrization. The effect of the angles of contact surfaces on the wheel dynamics and on the level of the self-excitation suppression will be discussed herein.

In this article, the coupled Drinfeld–Sokolov–Wilson equation under investigation base on computational approach named extension of modified rational expansion approach. By this computational approach secured various kinds of solitons named kink solitons, dark solitons, anti kink solitons, periodic solitons, bright solitons, kink dark solitons, kink bright solitons, anti kink dark solitons, anti kink bright solitons for coupled DSW system. The calculated results are interesting, precise, novel, and different which have not been secured in the previous research. We represent the graphical behaviour of determined solutions by 2-D, 3-D and contour through computational software. The determined results may helpful and play significant role in the study of nonlinear behaviour in various branches of physical sciences such as laser optics, communication system, fluid dynamics, transfer of heat, shallow water waves, acoustics, optics and many others. The constructed results prove that proposed computational approach is concise, powerful, and straightforward for securing the solitons results of other nonlinear partial differential equations.

We report a new batch of wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation which represents a coupled system of nonlinear partial differential equations (NLPDEs). Firstly by making a travelling wave ansatz, we decouple the system and obtain a second-order ordinary differential equation (ODE). Thereafter we perform phase space and bifurcation analysis of that second-order ODE and proceed to construct the general solution for the envelope of the wave packet. The solutions are expressed in terms of the Jacobi elliptic sine function from which one can obtain solitary wave (particular) solutions by imposing appropriate conditions on the roots of certain quartic polynomials as discussed thereafter.

A generalization of the time-delayed Burgers–Fisher equation is studied. This partial differential equation appears in many physical and biological problems describing the interaction between reaction, diffusion, and convection. New travelling wave solutions are obtained. The solutions are derived in a systematic way by applying the multi-reduction method to the symmetry-invariant conservation laws. The translation-invariant conservation law yields a first integral, which is a first-order Chini equation. Under certain conditions on the coefficients of the equation, the Chini type equation obtained can be solved, yielding travelling wave solutions expressed in terms of the Lerch transcendent function. For a special case, the first integral becomes a Riccati equation, whose solutions are given in terms of Bessel functions, and for a special case of the parameters, the solutions are given in terms of exponential, trigonometric, and hyperbolic functions. Furthermore, a complete classification of the zeroth-order local conservation laws is obtained. To the best of our knowledge, our results include new solutions that have not been previously reported in the literature. [ABSTRACT FROM AUTHOR]

Identification of fault localization in microgrid (MG) network using travelling wave (TW) mainly depends on the propagation velocity (ϑ ) of the reflected wave and type of mother wavelet chosen for extraction TW using discrete wavelet transform (DWT). Estimation of ϑ in non-homogeneous MG network and selection of the appropriate mother wavelet are a challenging task. This paper proposes a method to overcome the defined challenges in a non-homogeneous MG network. Proposed method majorly works in two parts: i) fault detection, faulty section identification and ii) fault location scheme in a medium voltage MG network. The first part utilizes added decoupled RMS currents (ADRMSC) values to detect and identify faulty section. Second part utilizes the consecutive sample difference approach (CSDA), and first arrival time instants of travelling wave (TW) at section terminals, computed using discrete wavelet transform (DWT) to locate the fault. Proposed scheme depends on the capture of time instants, which makes it least affected by the change in mother wavelets. The proposed scheme also performs well for a non-homogeneous system as it is independent of TW propagation velocity to locate the fault. The performance of the proposed method is validated on the non-homogeneous IEEE-33 bus system in EMTDC/PSCAD for various case studies which includes changes in fault parameters such as fault resistance, fault inception angle and noise level and found effective even with the change in mother wavelets. [ABSTRACT FROM AUTHOR]

Background: Kinetic Inductance Travelling Wave Parametric Amplifiers (KITWPAs) are a variant of superconducting amplifier that can potentially achieve high gain with quantum-limited noise performance over broad bandwidth, which is important for many ultra-sensitive experiments. In this paper, we present a novel modelling technique that can better capture the electromagnetic behaviour of a KITWPA without the translation symmetry assumption, allowing us to flexibly explore the use of more complex transmission line structures and better predict their performance. Methods: In order to design a KITWPA with optimal performance, we investigate the use of different superconducting thin film materials, and compare their pros and cons in forming a high-gain low-loss medium feasible for amplification. We establish that if the film thickness can be controlled precisely, the material used has less impact on the performance of the device, as long as it is topologically defect-free and operating within its superconducting regime. With this insight, we propose the use of Titanium Nitride (TiN) film for our KITWPA as its critical temperature can be easily altered to suit our applications. We further investigate the topological effect of different commonly used superconducting transmission line structures with the TiN film, including the effect of various non-conducting materials required to form the amplifier. Results: Both of these comprehensive studies led us to two configurations of the KITWPA: 1) A low-loss 100 nm thick TiN coplanar waveguide amplifier, and 2) A compact 50 nm TiN inverted microstrip amplifier. We utilise the novel modelling technique described in the first part of the paper to explore and investigate the optimal design and operational setup required to achieve high gain with the broadest bandwidth for both KITWPAs, including the effect of loss. Conclusions: Finally, we conclude the paper with the actual layout and the predicted gain-bandwidth product of our KITWPAs.

While seizure activity may be electrographically widespread, increasing evidence has suggested that ictal discharges may in fact represent travelling waves propagated from a focal seizure source. Interictal epileptiform discharges (IEDs) are an electrographic manifestation of excessive hypersynchronization of cortical activity that occur between seizures and are considered a marker of potentially epileptogenic tissue. The precise relationship between brain regions demonstrating IEDs and those involved in seizure onset, however, remains poorly understood. Here, we hypothesize that IEDs likewise reflect the receipt of travelling waves propagated from the same regions which give rise to seizures. Forty patients from our institution who underwent invasive monitoring for epilepsy, proceeded to surgery and had at least one year of follow-up were included in our study. Interictal epileptiform discharges were detected using custom software, validated by a clinical epileptologist. We show that IEDs reach electrodes in sequences with a consistent temporal ordering, and this ordering matches the timing of receipt of ictal discharges, suggesting that both types of discharges spread as travelling waves. We use a novel approach for localization of ictal discharges, in which time differences of discharge receipt at nearby electrodes are used to compute source location; similar algorithms have been used in acoustics and geophysics. We find that interictal discharges co-localize with ictal discharges. Moreover, interictal discharges tend to localize to the resection territory in patients with good surgical outcome and outside of the resection territory in patients with poor outcome. The seizure source may originate at, and also travel to, spatially distinct IED foci. Our data provide evidence that interictal discharges may represent travelling waves of pathological activity that are similar to their ictal counterparts, and that both ictal and interictal discharges emerge from common epileptogenic brain regions. Our findings have important clinical implications, as they suggest that seizure source localizations may be derived from interictal discharges, which are much more frequent than seizures. [ABSTRACT FROM AUTHOR]

Psychedelic drugs are potent modulators of conscious states and therefore powerful tools for investigating their neurobiology. N,N, Dimethyltryptamine (DMT) can rapidly induce an extremely immersive state of consciousness characterized by vivid and elaborate visual imagery. Here, we investigated the electrophysiological correlates of the DMT-induced altered state from a pool of participants receiving DMT and (separately) placebo (saline) while instructed to keep their eyes closed. Consistent with our hypotheses, results revealed a spatio-temporal pattern of cortical activation (i.e. travelling waves) similar to that elicited by visual stimulation. Moreover, the typical top-down alpha-band rhythms of closed-eyes rest were significantly decreased, while the bottom-up forward wave was significantly increased. These results support a recent model proposing that psychedelics reduce the 'precision-weighting of priors', thus altering the balance of top-down versus bottom-up information passing. The robust hypothesis-confirming nature of these findings imply the discovery of an important mechanistic principle underpinning psychedelic-induced altered states.

Growing evidence suggests that travelling waves are functionally relevant for cognitive operations in the brain. Several electroencephalography (EEG) studies report on a perceptual alpha-echo, representing the brain response to a random visual flicker, propagating as a travelling wave across the cortical surface. In this study, we ask if the propagating activity of the alpha-echo is best explained by a set of discrete sources mixing at the sensor level rather than a cortical travelling wave. To this end, we presented participants with gratings modulated by random noise and simultaneously acquired the ongoing MEG. The perceptual alpha-echo was estimated using the temporal response function linking the visual input to the brain response. At the group level, we observed a spatial decay of the amplitude of the alpha-echo with respect to the sensor where the alpha-echo was the largest. Importantly, the propagation latencies consistently increased with the distance. Interestingly, the propagation of the alpha-echoes was predominantly centro-lateral, while EEG studies reported mainly posterior-frontal propagation. Moreover, the propagation speed of the alpha-echoes derived from the MEG data was around 10 m/s, which is higher compared to the 2 m/s reported in EEG studies. Using source modelling, we found an early component in the primary visual cortex and a phase-lagged late component in the parietal cortex, which may underlie the travelling alpha-echoes at the sensor level. We then simulated the alpha-echoes using realistic EEG and MEG forward models by placing two sources in the parietal and occipital cortices in accordance with our empirical findings. The two-source model could account for both the direction and speed of the observed alpha-echoes in the EEG and MEG data. Our results demonstrate that the propagation of the perceptual echoes observed in EEG and MEG data can be explained by two sources mixing at the scalp level equally well as by a cortical travelling wave. Importantly, these findings should not be directly extrapolated to intracortical recordings, where travelling waves gradually propagate at a sub-millimetre scale.

The higher order diffusion can be understood as a generalization to the classical fickian diffusion. To account for such generalization, the Landau-Ginzburg free energy concept is applied leading to a fourth order spatial operator. This kind of diffusion induces a set of instabilities in the proximity of the critical points raising difficulties to study the convergence of Travelling Waves (TW) solutions. This paper aims at introducing a system of two species driven by a mutual interaction towards prospering and with a logistic term in their respective reactions. Previous to any analytical finding of TW solutions, the instabilities of such solutions are studied. Afterwards, the Geometric Perturbation Theory is applied to provide means to search for a linearized hyperbolic manifold in the proximity of the equilibrium points. The homotopy graphs for each of the flows to the hyperbolic manifolds are provided, so that analytical solutions can be obtained in the proximity of the critical points. Additionally, the set of eigenvalues in the homotopy graphs tend to cluster and synchronize for increasing values of the TW-speed.

The goal of this paper is to provide analytical assessments to a fluid flowing in a porous medium with a non-linear diffusion linked to a degenerate diffusivity. The viscosity term is formulated with an Eyring-Powell law, together with a non-homogeneous diffusion typical of porous medium equations (as known in the theory of partial differential equations). Further, the equation is supplemented with an absorptive reaction term of Darcy-Forchheimer, commonly used to model flows in porous medium. The work starts by analyzing regularity, existence and uniqueness of solutions. Afterwards, the problem is transformed to study travelling wave kind of solutions. An asymptotic expansion is considered with a convergence criteria based on the geometric perturbation theory. Supported by this theory, there exists an exponential decaying rate in the travelling wave profile. Such exponential behaviour is validated with a numerical assessment. This is not a trivial result given the degenerate diffusivity induced by the non-linear diffusion of porous medium type and suggests the existence of regularity that can serve as a baseline to construct numerical or energetic approaches.

Exact solutions of nonlinear equations have got formidable attraction of researchers because these solutions demonstrate the physical behaviour of a model. In this paper, we focus on extracting some new exact solutions of a (4+1)-dimensional Davey–Stewartson-Kadomtsev–Petviashvili (DSKP) equation. To find new travelling wave solutions of the DSKP equation, we use (G′G′+G+A)-expansion technique. The obtained solutions are in the form of the exponential and trigonometric functions. We obtain different kinds of waves solutions for specific values of parameters. We simulate the achieved solutions in 3D and 2D plots.

Existing comparative studies between individual-based models of growing cell populations and their continuum counterparts have mainly been focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However, significant intercellular phenotypic variability is commonly observed in cellular systems. In light of these considerations, we develop here an individual-based model for the growth of phenotypically heterogeneous cell populations. In this model, the phenotypic state of each cell is described by a structuring variable that captures intercellular variability in cell proliferation and migration rates. The model tracks the spatial evolutionary dynamics of single cells, which undergo pressure-dependent proliferation, heritable phenotypic changes and directional movement in response to pressure differentials. We formally show that the continuum limit of this model comprises a non-local partial differential equation for the cell population density function, which generalises earlier models of growing cell populations. We report on the results of numerical simulations of the individual-based model which illustrate how proliferation-migration tradeoffs shaping the evolutionary dynamics of single cells can lead to the formation, at the population level, of travelling waves whereby highly-mobile cells locally dominate at the invasive front, while more-proliferative cells are found at the rear. Moreover, we demonstrate that there is an excellent quantitative agreement between these results and the results of numerical simulations and formal travelling-wave analysis of the continuum model, when sufficiently large cell numbers are considered. We also provide numerical evidence of scenarios in which the predictions of the two models may differ due to demographic stochasticity, which cannot be captured by the continuum model. This indicates the importance of integrating individual-based and continuum approaches when modelling the growth of phenotypically heterogeneous cell populations.

A generalization of the time-delayed Burgers–Fisher equation is studied. This partial differential equation appears in many physical and biological problems describing the interaction between reaction, diffusion, and convection. New travelling wave solutions are obtained. The solutions are derived in a systematic way by applying the multi-reduction method to the symmetry-invariant conservation laws. The translation-invariant conservation law yields a first integral, which is a first-order Chini equation. Under certain conditions on the coefficients of the equation, the Chini type equation obtained can be solved, yielding travelling wave solutions expressed in terms of the Lerch transcendent function. For a special case, the first integral becomes a Riccati equation, whose solutions are given in terms of Bessel functions, and for a special case of the parameters, the solutions are given in terms of exponential, trigonometric, and hyperbolic functions. Furthermore, a complete classification of the zeroth-order local conservation laws is obtained. To the best of our knowledge, our results include new solutions that have not been previously reported in the literature.

It is the objective to provide a mathematical treatment of a model to predict the behaviour of an invasive specie proliferating in a domain, but with a certain hostile zone. The behaviour of the invasive is modelled in the frame of a non-linear diffusion (of Porous Medium type) equation with non-Lipschitz and heterogeneous reaction. First of all, the paper examines the existence and uniqueness of solutions together with a comparison principle. Once the regularity principles are shown, the solutions are studied within the Travelling Waves (TW) domain together with stability analysis in the frame of the Geometric Perturbation Theory (GPT). As a remarkable finding, the obtained TW profile follows a potential law in the stable connection that converges to the stationary solution. Such potential law suggests that the pressure induced by the invasive over the hostile area increases over time. Nonetheless, the finite speed, induced by the non-linear diffusion, slows down a possible violent invasion.

The intention along the presented analysis is to explore existence, uniqueness, regularity of solutions and travelling waves profiles to a Darcy-Forchheimer fluid flow formulated with a non-linear diffusion. Such formulation is the main novelty of the present study and requires the introduction of an appropriate mathematical treatment to deal with the introduced degenerate diffusivity. Firstly, the analysis on existence, regularity and uniqueness is shown upon definition of an appropriate test function. Afterwards, the problem is formulated within the travelling wave domain and analyzed close the critical points with the Geometric Perturbation Theory. Based on this theory, exact and asymptotic travelling wave profiles are obtained. In addition, the Geometric Perturbation Theory is used to provide evidences of the normal hyperbolicity in the involved manifolds that are used to get the associated travelling wave solutions. The main finding, which is not trivial in the non-linear diffusion case, is related with the existence of an exponential profile along the travelling frame. Eventually, a numerical exercise is introduced to validate the analytical solutions obtained.

The higher order diffusion can be understood as a generalization to the classical fickian diffusion. To account for such generalization, the Landau-Ginzburg free energy concept is applied leading to a fourth order spatial operator. This kind of diffusion induces a set of instabilities in the proximity of the critical points raising difficulties to study the convergence of Travelling Waves (TW) solutions. This paper aims at introducing a system of two species driven by a mutual interaction towards prospering and with a logistic term in their respective reactions. Previous to any analytical finding of TW solutions, the instabilities of such solutions are studied. Afterwards, the Geometric Perturbation Theory is applied to provide means to search for a linearized hyperbolic manifold in the proximity of the equilibrium points. The homotopy graphs for each of the flows to the hyperbolic manifolds are provided, so that analytical solutions can be obtained in the proximity of the critical points. Additionally, the set of eigenvalues in the homotopy graphs tend to cluster and synchronize for increasing values of the TW-speed. [ABSTRACT FROM AUTHOR]

The goal of this paper is to provide analytical assessments to a fluid flowing in a porous medium with a non-linear diffusion linked to a degenerate diffusivity. The viscosity term is formulated with an Eyring-Powell law, together with a non-homogeneous diffusion typical of porous medium equations (as known in the theory of partial differential equations). Further, the equation is supplemented with an absorptive reaction term of Darcy-Forchheimer, commonly used to model flows in porous medium. The work starts by analyzing regularity, existence and uniqueness of solutions. Afterwards, the problem is transformed to study travelling wave kind of solutions. An asymptotic expansion is considered with a convergence criteria based on the geometric perturbation theory. Supported by this theory, there exists an exponential decaying rate in the travelling wave profile. Such exponential behaviour is validated with a numerical assessment. This is not a trivial result given the degenerate diffusivity induced by the non-linear diffusion of porous medium type and suggests the existence of regularity that can serve as a baseline to construct numerical or energetic approaches. [ABSTRACT FROM AUTHOR]

The goal of this study is to provide analytical and numerical assessments to a fluid flow based on an Eyring–Powell viscosity term and a Darcy–Forchheimer law in a porous media. The analysis provides results about regularity, existence and uniqueness of solutions. Travelling wave solutions are explored, supported by the Geometric Perturbation Theory to build profiles in the proximity of the equation critical points. Finally, a numerical routine is provided as a baseline for the validity of the analytical approach presented for low Reynolds numbers typical in a porous medium. [ABSTRACT FROM AUTHOR]

Most of the fault wave localization methods are based on the analysis of line current transformed by current transformers and are limited to high voltage grids. Fault wave localization in medium voltage grids is still being developed. This paper presents a new real-time algorithm for the identification of travelling waves in a distribution grid using voltage signal and the short-time matrix pencil method. To obtain the secondary side voltage waveforms at substation, the model of a resistive voltage sensor based on the broadband measurements from 10 Hz to 20 MHz was developed. The tested sensor amplifies the frequencies associated with travelling waves more than utility frequency allowing for the identification. Short-circuit simulations on the IEEE 34-bus feeder was performed to test the algorithm. The developed method can detect even the waves of low amplitude. [ABSTRACT FROM AUTHOR]

Background: An earlier oscillator model for the generation of spontaneous otoacoustic emissions (SOAEs) from the lizard ear is extended with a connection of the oscillators to the basilar papilla, to make it possible that these SOAEs can be transported to the tympanic membrane, to be emitted. Material and methods: The generators of spontaneous otoacoustic emissions are modelled as a one-dimensional array of Hopf-resonators. The resonators (or oscillators) are coupled to their neighbours, and to the basilar papilla. The papilla is modelled as a rigid structure, that is flexibly connected to its surroundings. Results: Frequency spectra are given for different sets of coupling parameters, both for nearest neighbour coupling of the oscillators, and for coupling to the papilla, and also after the introduction of irregularities in the damping of the oscillators. Waterfall and density plots show clustering of the oscillators in frequency plateaus, and entrainment of a cluster of oscillators by an externally applied sinusoidal force. All these model outcomes correspond with characteristics of SOAEs emitted by real lizard ears. Conclusions: The present model is a useful extension of an earlier model. Because its characteristics differ from that of a model that is used to describe the generation of SOAEs by mammalian ears, it revives the discussion whether different models are needed for SOAE generation in different animal species [ABSTRACT FROM AUTHOR]

The goal of the present study is to characterize solutions under a travelling wave formulation to a degenerate Fisher-KPP problem. With the degenerate problem, we refer to the following: a heterogeneous diffusion that is formulated with a high order operator; a non-linear advection and non-Lipstchitz spatially heterogeneous reaction. The paper examines the existence of solutions, uniqueness and travelling wave oscillatory properties (also called instabilities). Such oscillatory behaviour may lead to negative solutions in the proximity of zero. A numerical exploration is provided with the following main finding to declare: the solutions keeps oscillating in the proximity of the null stationary solution due to the high order operator, except if the reaction term is quasi-Lipschitz, in which it is possible to define a region where solutions are positive locally in time. [ABSTRACT FROM AUTHOR]

We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis in the fast switching regime shows that the total cell density in the two-population go-or-grow model can be described in terms of a single reaction–diffusion equation with density-dependent diffusion and proliferation. Using the connection to single-population models, we study travelling wave solutions, showing that the wave speed in the go-or-grow model is always bounded by the wave speed corresponding to the well-known Fisher–KPP equation. [ABSTRACT FROM AUTHOR]

A thermophilic suspension of nanoparticles heated from below exhibits a complex stability diagram determined by the competition between the stabilizing flux of nanoparticles induced by thermophoresis and the destabilizing flux determined by thermal convection. We investigate Rayleigh-Bénard convection in a suspension of highly thermophilic nanoparticles with large negative separation ratio ψ = −3.5 heated from below. We show that transient localized states appear in the range of Rayleigh numbers 2200

In this work we investigate well-posedness for the partial differential equation stemming from the balance of linear momentum for an implicit constitutive relation that can describe the response of porous elastic solids whose material moduli depend on the density. We study heteroclinic travelling waves and obtain closed form analytic solutions for the resulting ordinary differential equation. Finally, we consider some special solutions for the partial differential equation and solve the resulting equations numerically. [ABSTRACT FROM AUTHOR]

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the self-similar structure that permits showing the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive species predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support). [ABSTRACT FROM AUTHOR]

We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.

In this work we focus on the numerical solution of a higher order bidirectional nonlinear model of Boussinesq type involving a nonlocal operator. Based on a von Neumann stability analysis for the linearized problem, an efficient and stable scheme for the nonlinear system is proposed. Our method is based on a numerical scheme known from the literature that solves satisfactorily a lower order linear system. Additionally, approximate periodic travelling wave solutions profiles for the higher order nonlinear system are presented. Such approximate travelling wave solutions are obtained from a solitary wave family of solutions for the Intermediate Long Wave (ILW) equation and the regularized Intermediate Long Wave (rILW) equation.

This paper concerns the invasion dynamics of the lattice pioneer-climax competition model with parameter regions in which the system is non-monotone. We estimate the spreading speeds and establish appropriate conditions under which the spreading speeds are linearly selected. Moreover, the existence of travelling waves is determined by constructing suitable upper and lower solutions. It shows that the spreading speed coincides with the minimum wave speed of travelling waves if the diffusion rate of the invasive species is larger or equal to that of the native species. Our results are new to estimate the spreading speed of non-monotone lattice pioneer-climax systems, and the techniques developed in this work can be used to study the invasion dynamics of the pioneer-climax system with interaction delays, which could extend the results in the literature. The analysis replies on the construction of auxiliary systems, upper and lower solutions, and the monotone dynamical system approach.

In this letter, an alternative solution for travelling wave based directional relaying scheme is presented by utilizing the prefault voltage sample acquired at a much lower sampling rate along with current travelling wave. There is no requirement of voltage travelling waves for the method. The performance of the proposed method is evaluated for faults simulated on a 400 kV transmission network which reveals its advantage for faults when change in voltage signal is low. The proposed method is independent of the transient response of the capacitive voltage transformer. [ABSTRACT FROM AUTHOR]

The aim of this work was to provide a formulation of a non-linear diffusion model with forced convection in the form of a reaction–absorption system. The model was studied with analytical and numerical approaches in the frame of the parabolic operators theory. In addition, the solutions are applied to a gas interaction phenomenon with the intention of producing an inerted ullage in an Airbus A320 aircraft centre fuel tank. We made use of the travelling wave (TW) solutions approach to study the existence of solutions, stability and the precise evolution of profiles. The application exercise sought to answer a key question for aerospace sciences which can be formulated as the time required to ensure an aircraft fuel tank is safe (inerted) to prevent explosion due to the presence of oxygen in the tank ullage. [ABSTRACT FROM AUTHOR]

Traveling waves of permanent form with compact support are possible in several nonlinear partial nonlinear differential equations and this, mainly, along two pathways: A pure nonlinearity stronger than quadratic in the higher order gradient terms describing the mathematical model of the phenomena or a special inhomogeneity in quadratic gradient terms of the model. In the present note we perform a rigorous analysis of the mathematical structure of compactification via a generalization of a classical theorem by Weierstrass. Our mathematical analysis allows to explain in a rigorous and complete way the presence of compact structures in nonlinear partial differential equations 1 + 1 dimensions.

The goal of this study is to provide analytical and numerical assessments to a fluid flow based on an Eyring–Powell viscosity term and a Darcy–Forchheimer law in a porous media. The analysis provides results about regularity, existence and uniqueness of solutions. Travelling wave solutions are explored, supported by the Geometric Perturbation Theory to build profiles in the proximity of the equation critical points. Finally, a numerical routine is provided as a baseline for the validity of the analytical approach presented for low Reynolds numbers typical in a porous medium.

Most of the fault wave localization methods are based on the analysis of line current transformed by current transformers and are limited to high voltage grids. Fault wave localization in medium voltage grids is still being developed. This paper presents a new real-time algorithm for the identification of travelling waves in a distribution grid using voltage signal and the short-time matrix pencil method. To obtain the secondary side voltage waveforms at substation, the model of a resistive voltage sensor based on the broadband measurements from 10 Hz to 20 MHz was developed. The tested sensor amplifies the frequencies associated with travelling waves more than utility frequency allowing for the identification. Short-circuit simulations on the IEEE 34-bus feeder was performed to test the algorithm. The developed method can detect even the waves of low amplitude.

The goal of the present study is to characterize solutions under a travelling wave formulation to a degenerate Fisher-KPP problem. With the degenerate problem, we refer to the following: a heterogeneous diffusion that is formulated with a high order operator; a non-linear advection and non-Lipstchitz spatially heterogeneous reaction. The paper examines the existence of solutions, uniqueness and travelling wave oscillatory properties (also called instabilities). Such oscillatory behaviour may lead to negative solutions in the proximity of zero. A numerical exploration is provided with the following main finding to declare: the solutions keeps oscillating in the proximity of the null stationary solution due to the high order operator, except if the reaction term is quasi-Lipschitz, in which it is possible to define a region where solutions are positive locally in time.

Abstract Background Segmentation, the subdivision of the major body axis into repeated elements, is considered one of the major evolutionary innovations in bilaterian animals. In all three segmented animal clades, the predominant segmentation mechanism is sequential segmentation, where segments are generated one by one in anterior–posterior order from a posterior undifferentiated zone. In vertebrates and arthropods, sequential segmentation is thought to arise from a clock-and-wavefront-type mechanism, where oscillations in the posterior growth zone are transformed into a segmental prepattern in the anterior by a receding wavefront. Previous evo-devo simulation studies have demonstrated that this segmentation type repeatedly arises, supporting the idea of parallel evolutionary origins in these animal clades. Sequential segmentation has been studied most extensively in vertebrates, where travelling waves have been observed that reflect the slowing down of oscillations prior to their cessation and where these oscillations involve a highly complex regulatory network. It is currently unclear under which conditions this oscillator complexity and slowing should be expected to evolve, how they are related and to what extent similar properties should be expected for sequential segmentation in other animal species. Results To investigate these questions, we extend a previously developed computational model for the evolution of segmentation. We vary the slope of the posterior morphogen gradient and the strength of gene expression noise. We find that compared to a shallow gradient, a steep morphogen gradient allows for faster evolution and evolved oscillator networks are simpler. Furthermore, under steep gradients, damped oscillators often evolve, whereas shallow gradients appear to require persistent oscillators which are regularly accompanied by travelling waves, indicative of a frequency gradient. We show that gene expression noise increases the likelihood of evolving persistent oscillators under steep gradients and of evolving frequency gradients under shallow gradients. Surprisingly, we find that the evolutions of oscillator complexity and travelling waves are not correlated, suggesting that these properties may have evolved separately. Conclusions Based on our findings, we suggest that travelling waves may have evolved in response to shallow morphogen gradients and gene expression noise. These two factors may thus also be responsible for the observed differences between different species within both the arthropod and chordate phyla.